Jaynes avoids P(A|B) for "probability of A given evidence B" and P(B) for "probability of B", preferring P(A|BX) and P(B|X) where X is one's background knowledge. This and the above leads naturally to the question of ~X: the situation in which one's "background knowledge" is false.

Assume that background knowledge X is the conjunction of a finite number of propositions. ~X is true if any of these propositions is false. If we can factor X into YZ where Y is the portion we suspect of being false — that is, if we can isolate for testing a portion of those beliefs we previously treated as "background knowledge" — then we can ask about P(A|BYZ) and P(A|B·~Y·Z).

## Comments (128)

OldJaynes avoids P(A|B) for "probability of A given evidence B" and P(B) for "probability of B", preferring P(A|BX) and P(B|X) where X is one's background knowledge. This and the above leads naturally to the question of ~X: the situation in which one's "background knowledge" is false.

Assume that background knowledge X is the conjunction of a finite number of propositions. ~X is true if

anyof these propositions is false. If we can factor X into YZ where Y is the portion we suspect of being false — that is, if we can isolate for testing a portion of those beliefs we previously treated as "background knowledge" — then we can ask about P(A|BYZ) and P(A|B·~Y·Z).